For AgentNet in all of the tasks, we use AdamW optimizer [1]} with a weight decay of \(0.1\) . We set the initial learning rate to \(10^{-4}\)  and decay it over the whole training to \(10^{-11}\)  using a cosine schedule. We also clip the global gradient norm to 1. In all of the cases, Gumbel-Softmax temperature is set to \(\frac{2}{3}\)  as this has been suggested as a robust choice when the distribution has only a few categories [2]}.
